What is the difference between out of distribution detection and anomaly detection?
You observation is correct although the terminology needs a little explaining.
The term 'out-of-distribution' (OOD) data refers to data that was collected at a different time, and possibly under different conditions or in a different environment, then the data collected to create the model.  They may say that this data is from a 'different distribution'.
Data that is in-distribution can be called novelty data.  Novelty detection is when you have new data (i.e. OOD) and you want to know whether or not it is in-distribution.  You want to know if it looks like the data you trained on.
Anomaly detection is when you test your data to see if it is different than what you trained the model.  Out-of-distribution detection is essentially running your model on OOD data.  So one takes OOD data and does novelty detection or anomaly detection (aka outlier detection).
Below is a figure from What is anomaly detection?

In time series modeling, the term 'out-of-distribution' data is analogous to 'out-of-sample' data and 'in-distribution' data is analogous with 'in-sample' data.